Binding equations

Fig. 15 Plot of kobs vs. [Zn2+]total for the decomposition of 32 (8 x HP6 mol dm 3) in anhydrous ethanol at [ OEt]/[Zn2+]totai = 0.5. Fitting the data to a universal binding equation gives an apparent dissociation constant Kd for Zn. 32 of (6.2 0.1) x 10 5moldm 3 and a kmax of 1.88 x 10 2s 1 r2 = 0.9811. Reproduced with permission from ref. 85.

The mathematical treatment of each of the fluorescence curves shown in O Figure 5-5 is identical. First nonspecific effects must be subtracted so that in each case we have a relationship between the concentration of ligand and the change in fluorescence. The binding equation is formally identical to the terminology for... 

A ligand binding plot (1/n versus l/[Aj) that permits one to determine the number of ligand binding sites and the dissociation constant for the protein-ligand complex. The typical binding equation for -independent sites is... 

Nichol and Winzor described the binding equations that apply to such hgand-induced changes in receptor oligomerization. They also presented the following equation to describe the joint operation of allosteric ligand binding cooperativity and receptor self-association. 

The derivation of equilibrium ligand binding equations for this model involves the following assumptions First, the protein is oligomeric and contains a finite number of identical subunits (called protomers). Second, the protein exists in two different symmetrical states (historically re-... 

Terms appearing in binding equations describing the linked equilibria for the binding of a ligand (or proton)... 

The free energy of binding is a combination of both the enthalpy and entropy of binding (Equation 9.3). 

Figure 9. Concentration-response curve of sucrose in the presence of methyl a-D-glucopyranoside (MaG). The solid lines are theoretical curves obtained from an equation describing the competitive interaction of two substances with a single receptor site (see below). Data points for sucrose alone ( ) sucrose + 0.1 M MaG (A) sucrose + 0.3 M MaG, sucrose + 1.0 M MaG, O MaG alone Dashed line is the theoretical curve drawn from the binding equation for MaG. Kj for sucrose (0.05 M) and Kd for MaG (0.18 M) were determined from the Beid-ler plot (see inset). CRst, for sucrose — 0.052 and for MaG = 0.18 (13).

Z.-X. Wang and R.-F. Jiang, A Novel Two-Site Binding Equation Presented in Terms of the Total Ligand Concentration, FEBS Lett., 392, 245 (1996). 

In the high affinity assay for each compound, five assay points are generated and evaluated via a Scatchard type analysis using a linearized binding equation. Rearrangement of... 

When n = 1, Eq. 9.45) yields a rectangular hyperbola. Recall that the Michaelis-Menten expression is written with Km being equivalent to (and having the units of) a dissociation constant, whereas binding equations, such as the Hill equation, are usually written with association constants (their numerical values being the reciprocal of the corresponding dissociation constants). 

Figure . A.) A binding curve for TPPI using the 37 base-pair sequence. Thedatawerefit using the binding equation of Limetal. (2). Error bars represent the error in R based on a 1 nun emu-in measuring distances on the autoradiogram. B.) AScatchardplotofthesamedata which were fit uang equation 1.

Figure 3. Binding isothenns for Xfin-3 l(S-S) (closed circles) and Xfin-3 (open drdes) using the 19 base-pair sequence. The data were fit using the binding equation of Lim et al. (2).

The Lineweaver-Burk reciprocal plot is not the only linear transformation of the basic velocity (or ligand binding) equation. Indeed, under some circumstances one of the other linear plots described below may be more suitable or may yield more reliable estimates of the kinetic constants. For example, the Hanes-Woolf plot of [S]/u versus [S] may be more convenient... 

Equation 75 (as all others derived from rapid equilibrium assumptions) is really an equilibrium binding equation that gives the ratio of occupied to total sites. We obtain a velocity equation by assuming that the velocity is proportional to the concentration of occupied sites. In other words, a velocity equadon is obtained when we equate Ys to v/Vm xi... 

Eq. 4 is derived based on an exact solution to the binding equation for E and I. Thus, the fit of Eq. 4 to inhibition data results in an estimate of both /l and IC50 value. The kinetics of tight-binding inhibitors are presented in more detail in ref. 12. 

Equation 5.48) can be deduced from the reactions of surfactant adsorption and counterion binding (Equations 5.51 and 5.54). (Eor / < 0.1 M we have y 1 and then activities and concentrations of the ionic species coincide.)... 

The plot of log[Y/(l - Y)] versus log[L] is linear (Fig. 9.3) with a slope of n. The all-or-none binding assumes extreme cooperativity in ligand binding. Under such conditions n should equal the number of sites within the protein. Few proteins exhibit extreme cooperativity. Therefore, the value for n is usually less than the number of sites but, when positive cooperativity occurs, n is greater than 1. In the case of negative cooperativity n is less than 1. An n value of 1 reduces the fractional saturation for the Hill equation (Equation 9.7) to that of simple ligand binding (Equation 9.4). 

Despite differences in the chemical nature of the active sites, three classes of natural oxygen carriers display amazing similarities in thermodynamic and kinetic parameters that characterize dioxygen binding. All noncooperative proteins or isolated subunits of oligomeric oxygen carriers show reversible 1 1 02 binding (Equation 4.5). 

Note that Eq. (28a) is the same as the transient solution to the deterministic binding equation with C0 = 0 [Eq. (6)]. 

Shift in lEP. The intrinsic constants may be used to estimate the composition of the oxide surface as a function of solution variables (pH, concentration of specifically adsorbable cations and anions). Without correcting for coulombic attraction or repulsion such calculations should give reasonable predictions only for surfaces that have a fixed surface charge of zero (or nearly zero). Hence, it should be possible to use intrinsic constants to predict shifts in lEP caused by specific cation and anion binding. Equation 20 gives the condition for zero fixed charge (lEP). 

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